Wednesday, August 25, 2010

You are a (small) open economy. If you borrow, you are a net importer of goods and services--you run a trade deficit. You may want to run a trade deficit for a long time, but ultimately, creditors will expect you to pay back what you owe. To make good on your promises, you will have to run a trade surplus at some point in the future. (Alternatively, you may wish to default, but let me ignore this possibility for now).

Setting the problem of default aside, the example above highlights a key property of what economists call an intertemporal budget constraint. Fancy words, but all it really means is that if you borrow today, you will have to pay back tomorrow. Applying the same principle to nations, it means that a trade deficit today will have to be matched by a trade surplus tomorrow. This principle suggests that "imbalances" in a country's international trade account are expected to be "temporary" (kind of like the "temporary" income tax measure of 1913?).

Sounds like good ol' common sense. And it probably applies to most countries. Except, maybe, for big and powerful economies, like the USA?

The US has had a growing trade deficit for the better part of the last 20 years; see Chart a (source). (The trend appears to have reversed a bit during the recent recession, but the most recent data show a move back to pre-recession levels.) For the most part, the flip side of the US trade deficit corresponds to a Chinese trade surplus. In short, the Chinese are working their pants off producing stuff and then exporting it to the US. In return, the US sends small denomination paper notes called USD (or US treasuries, representing promises to deliver future USD).

There is, as far as I can tell, no consensus on what is driving these interesting trade flows. Almost everyone seems to think that this imbalance is bad. Bad, bad, bad. (I mean, how can imbalance ever be good?). Someone must be getting screwed. Some believe that the American worker is the victim (see how clever those Chinese are...they have attained a full employment sweatshop equilibrium!). Others question the wisdom of Chinese trade policy (let's see, they ship us goods, we ship them paper, they ship us goods, we ship them more paper...hmm).

Well, maybe they're right. But before we capitulate to consensus opinion, I want to explore another possibility. Could it be that this exchange of goods for assets is mutually beneficial for the countries involved? (I abstract, of course, from the inevitable mix of winners and losers that are produced with any trade liberalization). And if so, how might this be?

In my previous post, I pointed to Ricardo Caballero's "Asset-Shortage Hypothesis" as one way to understand the "global imbalance" phenomenon. The basic idea is that there is a world "shortage" of assets that are perceived to be good collateral objects and/or good stores of value. The source of these shortages may ultimately be related to cross-country differences in property rights regimes (relatedly, the degree of financial development). If so, then local governments should address the problem directly. But if they do not, or if it takes time, then local agents may exhibit a demand for foreign-produced assets, like US dollars and US treasuries. Of course, to acquire such assets they will have to purchase them with exports of goods and services. This is not crazy; after all, there is also a huge domestic appetite for US treasuries in local repo and credit derivatives markets.

And so, perhaps countries like China simply find the USD useful and are therefore willing to pay for it (with exports). The US values foreign produce and so imports it (by exporting USD). Both countries experience gains from this trade.

A Simple Model

Let me describe one way to formalize the argument above. Consider a world consisting of two economies; a "domestic" economy and a "foreign" economy. Each country is populated by 2-period-lived overlapping generations (and an initial old generation, that lives for one period only). I use an OLG model for its analytical tractability--nothing I have to say here depends on the OLG structure, so don't get hung up on interpreting the model structure too literally.

The young in each country have a nonstorable endowment of output, y. The young derive a "little bit" of utility from consuming their endowment; but they would really rather consume output when they are old (i.e., they really value the output produced by the next generation of young people). This OLG structure is useful because it models a complete lack of double coincidence of wants among agents (and so, bilateral quid pro quo barter in goods is ruled out).

For the purpose of exposition, I take the asset shortage friction to an extreme. In particular, assume that there is only one asset, a fiat object called the USD, which is produced only in the domestic economy. For simplicity, I assume that the aggregate nominal stock of USD M remains fixed forever (it is easy to relax this assumption). Let ptdenote the price of output at date t measured in USD (i.e., the price-level).
I assume that the domestic population remains constant over time (normalize the population of domestic young agents to unity). I assume that the foreign population grows over time. Let Nt denote the population of foreign young agents at date t and assume that Nt+1 = nNt where n > 1 denotes the (gross) foreign population growth rate.

Note: we need not interpret N literally as population. It is simply a parameter that will index the foreign demand for USD. Likewise, n represents the rate of growth in that demand. A financial liberalization in the foreign sector, or some other innovation, can be modeled as a change in these parameters.

Autarky

Things are grim in the foreign sector; there is no trade at all. The young simply consume their endowment (they derive little pleasure from this) and the old go wanting. This is also an equilibrium outcome in the domestic economy. But there is also another equilibrium--one in which the fiat object is valued. In this equilibrium, the young sell their output to the old for USD (we endow the initial old with M). Hence, pt y = M for all t > 1. The young use the money accumulated in this manner to purchase the good they really desire (next period output). In this manner, money circulates as it facilitates welfare-improving trades. The (stationary) equilibrium price-level is constant over time,p = M / y. (Note: this is an example of a welfare-improving asset price bubble -- a result that commonly emerges in environments with asset-shortages).

Free trade

Well, if an asset price bubble (defined as an asset that trades above its fundamental value) is good for the domestic economy, might it also be good for the foreign economy (hence good for the world economy)? The answer is yes.

Imagine that trade is suddenly allowed to occur between these two economies at date 1. I like to think of the foreign sector at this point as being small relative to the domestic sector, so that 0 < N1 << 1. Of course, since n >1, the foreign sector is growing faster than the domestic economy. Left unchecked, this implies that the foreign sector will eventually swamp the domestic economy in size.

The date t foreign young agents will want to acquire USD. So they export their output y to the domestic economy for USD. The aggregate foreign demand for USD, measured in units of output, is Nt y. The domestic demand for USD is simply y. Hence, the relevant market-clearing condition at date t is now given by:

Since condition [1] must hold at all dates, it must also hold in period t + 1. Hence, M = (1 + Nt+1)pt+1 y . This latter equation, together with [1], allows us to derive an expression for the equilibrium inflation rate:

[2]pt+1 / pt = [ 1 + Nt ] / [ 1 + nNt ] < 1 (since n > 1 )

Condition [2] implies that the trade liberalization induces a deflation (a falling price level). In the limit, the deflation rate (the inverse of the inflation rate) approaches n from below. (Keep in mind that I am keeping the nominal supply of debt fixed in this experiment). Deflation in this model is neither good nor bad; it simply reflects the growing demand for USD and implies that the purchasing power of money rises over time.

That is, they will demand a fraction of the outstanding money supply (which is initially in the hands of the date 1 domestic old agents). To acquire these F1 dollars, they must export N1 y units of output to the domestic economy (to be consumed by the domestic old). The result is a trade balance surplus for the foreign economy and an offsetting trade balance deficit for the domestic economy.

As an aside, it is of some interest to note what happens next in the case of n = 1. What happens is that all international trade ceases. The USD acquired by foreigners in the initial period simply continue to circulate in the foreign economy as currency. Absent any changes, the domestic economy will forever be a debtor nation; and the foreign economy will forever be a creditor nation. On the other hand, it's not like the domestic economy "owes" the foreign economy anything. They did, after all, export USD, an asset that foreigners evidently find useful.

Let us now return to the case of n > 1. This case is even more interesting, because it implies that trade will continue into the indefinite future.

At date 2, the foreign demand for USD grows (in real terms) by (n - 1)N1 y. At date 3, this foreign demand will grow by (n -1)nN1 y. At date 4, it will grow by (n -1) n2 N1 y, and so on. For any arbitrary date t > 1, the additional real foreign demand for USD will grow by:

[4]xt = (n - 1) nt-2 N1 y

Assuming that the foreign sector keeps its borders open to international trade, equation [4] describes the flow of exports to the domestic economy in each period t. What is remarkable here, I think, is the theoretical possibility that these exports continue in perpetuity -- there the possibility of persistent and growing global imbalances in this world economy. Of course, going the other way are exports of USD. In the equilibrium under consideration, domestic residents peel away ever thinner slices of their remaining USD holdings and ship them to the foreign economy for imported goods. These thinner slices are able to buy the available imports because of the deflation, which increases the purchasing power of USD over time.

It would be of some interest, of course, to extend the model in a variety of ways. We might let the domestic government alter the supply of its assets (collecting seigniorage from the rest of the world). We might imagine a date at which the foreign demand for USD reverses, or even collapses. Etc., etc.

Conclusions

It's important that we not get carried away with a simple model, or ascribe too much importance to the Asset Shortage Hypothesis. There are almost certainly many other factors contributing to the phenomena we see developing around us.

Nevertheless, the hypothesis -- and the way in which I formalized it here -- may be an important contributing factor to the "global imbalances" phenomenon. If it is, then perhaps this is one way to interpret low US inflation rates (as opposed to a competing hypothesis, which explains inflation as the product of "output gaps"). Moreover, as the analysis above makes clear, global imbalances and asset price bubbles are not necessarily a "bad" thing. This does not, of course, mean that we can safely ignore these phenomena as they develop over time. Things might change and bubbles can burst. These are contingencies that policymakers need to plan for.

In a nutshell, the Asset-Shortage Hypothesis asserts that "good" assets are scarce; in particular, the type of assets that people would feel comfortable accepting as collateral for a loan, or as a store of value. It is remarkable how much might follow from this one property: asset price bubbles, low real interest rates, deflationary pressures, global imbalances, etc. In his presentation slides, Caballero concludes by saying that this simple ingredient can explain the main global macroeconomic phenomena of recent years. I want to argue that organizing one's thoughts around this general principle is probably a good way to think about macroeconomics in general.

In many ways, I think that the so-called New Monetarist (NM) brand of macroeconomic theory does precisely this. One of the fundamental frictions common to this class of models is the assumption of limited commitment (or limited enforcement--I'm not quite sure of the distinction). This friction can lead naturally to the asset-shortages emphasized by Caballero. A sticky price friction does not. (In the immortal words of Pierre-Simon Laplace: Je n'avais pas besoin de cette hypothèse-là. My own thoughts on the sticky price hypothesis can be located here).

Limited commitment/enforcement

The financial market is essentially a market in promises. In particular, debt constitutes a promise to repay. Of course, the flip side of debt is an extension of credit. And credit, in turn, requires a belief that promises will be kept (credere in Italian = to believe). The financial market would be a pretty boring place if people could simply be trusted to make good on their obligations (equivalently, if promises made could be enforced at zero cost). Unfortunately, things are not so boring.

It seems unlikely that people are intrinsically trustworthy. The supply of promises seems infinite. It is easy to ask for some favor now in exchange for a reward promised far into the future. Repaying a debt, on the other hand, appears rather more difficult. If they could do so with impunity, debtors are likely to renege on their promises. The result would be a suspension of credit. This is how a lack of commitment/enforcement leads to an asset shortage.

Institutional responses

Societies go to some length in adopting institutions that facilitate intertemporal trade. Perhaps the most basic of these institutions is reputation. The gain/loss of "reputation capital," leading to enhanced/diminished trading opportunities, will in many cases be sufficient to sustain debt. In many societies, the punishment for noncompliance (dishonor) frequently takes the form of social ostracism. (See what happens if you do not buy your fair share of beer for your drinking buddies, for example). Of course, more painful punishments are possible (knee-capping, whippings, debtors' prisons, etc.); but these enforcement mechanisms consume resources.

Unfortunately, reputational concerns are not always enough to promote good behavior (hello, Bernie Madoff). What other (relatively low-cost) ways might debt be sustained? It is worthwhile to note that a jilted creditor cannot eat an abandoned reputation; a transferable asset would surely taste better. It is for this reason, I think, that debt collateralized by some form of physical capital--an asset backed security--is one way to expand the supply of credit.

What makes good collateral?

Heck, I don't know. I think it may depend on both the physical and legal characteristics of the object in question. Physical capital is frequently used as collateral, whereas human capital is not. Why is that? Well, for one thing, physical capital is not likely to run away and hide from a claimant. But perhaps more importantly, indentured servitude is now legally prohibited in most jurisdictions.

Not all physical capital is created equally, of course. Capital that is fixed in place, like real estate, has some obvious advantages. Mobile capital (automobiles, consumer durables, inventory) seems less desirable to the extent that possessors can hide it from claimants. On the other hand, these latter goods are easily transferable; whereas transfers of titles to real estate may incur significant legal cost. But then again, none of this may really matter if legal stipulations prevent certain classes of capital goods from being used as collateral in the first place (bankruptcy laws frequently prevent creditors from seizing certain types of assets, like electric wheelchairs, pets, and even land in some jurisdictions).

In short, the system of property rights is likely to impinge on asset supply. To the extent that different jurisdictions possess different institutions, asset supply is likely to vary across countries. Agents or agencies belonging to countries whose institutions inhibit asset supply may wish to import (acquire) assets from other countries in exchange for goods and services. Is this a source of what some people refer to as global imbalances? Caballero seems to think so.

The use of capital in the payments system

If the use of unsecured credit is impossible, you must pay for an object you desire now in one of two ways (apart from barter). First, you may pay by relinquishing an asset. Alternatively, you may pay by issuing an IOU backed by an asset. Either way, you face an "asset-in-advance constraint."

For the moment, I want to think of the asset in question here as a form of physical capital, or non-counterfeitable, durable, and perfectly divisible titles to physical capital.

On the surface, these two methods of payment look rather different. The first entails immediate settlement, while the second entails delayed settlement. To the extent that the asset in question circulates widely as a device used for immediate settlement, it is called money (in this case, backed money). To the extent it is used in support of debt, it is called collateral. But while the monetary and credit transactions just described look different on the surface, they are equivalent in the sense that capital is used to facilitate transactions that might not otherwise have taken place.

If what I just said makes sense, then the theory of "money" (objects that circulate as exchange media in immediate settlement transactions) essentially boils down to a theory of optimal payment methods. The answer may depend on (among other things) security concerns and the available record-keeping technology. Small denomination paper is frequently used in small-value spot transactions. The use of more secure centralized record-keeping agencies are typically preferred for large-value transactions.

To put things another way, perhaps a theory of "money" may be of secondary importance. What is important from an economic perspective is that the gains to trade are realized whenever possible. The question is why objects belonging to certain asset classes are needed to facilitate trade. From this perspective, the line between "store of value" and "medium of exchange" appears somewhat blurred (at least to my sad eyes). In fact, I am becoming more convinced over time that it is the "store of value" properties of assets that render them more or less desirable as exchange media (broadly defined to include collateral). I expect that some of you may want to set me straight on this.

Private money systems

In a NM model with capital, titles to capital (or the capital itself, if it is divisible and transportable) can be as exchange media (unsecured credit markets are unavailable because people are assumed to lack commitment). For example, in Lagos and Rocheteau 2008, capital is used as money; in Ferraris and Watanabe 2007, capital is used as collateral. The properties of this class of models are in fact similar to those that arise in a standard overlapping generations (OLG) model with capital accumulation (this is one reason why I like to use OLG models to communicate the basic properties of these more elaborate setups).

Note: the papers just cited assume an "elastic" supply of capital (the stock of capital is adjustable). One might alternatively assume an "inelastic" supply of capital (as in a dividend producing Lucas tree). In the former case, the price of capital is fixed and quantity adjusts. In the latter case, the quantity of capital is fixed and price adjusts. Intermediate cases are possible, of course.

Anyway, it turns out that a private-money system can work pretty well in a NM model. Supporters of free-banking, or of laissez-faire in general, will no doubt be pleased with this result.

On the other hand (you knew this was coming), whether or not a private-money system can be expected to exhaust all feasible gains from trade depends on parameters that describe certain properties of the economic environment. One key parameter is the productivity of capital. This technology parameter essentially determines the ability of economy to overcome the asset-shortage problem (the root cause of which, I remind you, is the limited commitment/enforcement friction). So apart from institutional frictions, it appears that technology might be important as well (or perhaps we might interpret productivity broadly to encompass aspects of an economy's institutions).

In any case, let me describe the potential problem. Limited commitment implies that capital has an additional role to play. That is, apart from its usual role in production and storage, it possesses an additional service value through its ability to facilitate payments (as explained above). Hence, the demand for capital (more precisely, the subset of capital goods that constitute good collateral) will be higher than it would otherwise be in a frictionless economy.

Now, if the productivity of inelastic capital is not-so-good, or if the ability to create new capital is limited, then the economy will face an asset-shortage. If capital is inelastic, it price will rise. Indeed, its price may rise above its "fundamental" value (the present value of its net income flow). Market price above fundamental value is sometimes interpreted as a bubble; although, liquidity premium might be a better label; see Ricardo Lagos 2010. If capital is elastic, its supply will increase. The analog to the bubble in this case is an overaccumulation of capital (as in a standard OLG model). Either way, the effect of this "saving glut" is to put downward pressure on the real rate of interest. If the real rate falls below its "natural" rate, there is a dynamic inefficiency (the competitive equilibrium is inefficient).

A dynamic inefficiency may emerge even if the return to capital is expected to be high on average, as long as its expected short-run return drops sufficiently low on occasion (as in a severe recession). This is a line of enquiry that I am currently pursuing with my coauthor Fernando Martin. Interestly, the effect appears to have little, if anything, to do with risk-appetite (the result continues to hold for risk-neutral agents). A good property of collateral used in the payments system is what we call "value preservation," which reflects a desire for truncated downside risk. Let me try to explain this by example.

Imagine that you have in your possession a mortgage-backed security (MBS) that you like to use as collateral for your short-term lending needs. Moreover, imagine that you have no trouble borrowing all you need with this asset. Now, if the value of this asset appreciates, you are happy of course, but this in no way affects your borrowing. The story may be very different, of course, if the market price of your MBS suddenly plummets. Now you may be temporarily debt-constrained. Of course, tightening debt constraints are the hallmark of a credit crisis, or credit crunch (or un mancamento della credenza, as it was referred to in the Florentine banking crisis of 1341-1346; see Jesus Huerta De Soto). To the extent that credit contraction inhibits investment, we also have a familiar financial accelerator at work.

Let me summarize (before I get too carried away). Limited commitment generates a demand for assets with "good" properties, where "good" is defined in terms of an asset's ability to facilitate exchange. The value of the capital backing these assets varies over time. In normal-to-good times, this value variation does not really matter (debt constraints are slack). But in very bad times, it does (debt constraints bind). Despite the private sector's best efforts at generating AAA asset classes, it may not have the capacity to generate enough assets with the desired limited downside risk property. Shit happens.

A role for government debt

Of course, it's been known for a long time that dynamic inefficiency provides a rationale for the existence of government debt; see Peter Diamond 1965. If record-keeping is too costly (think small-value transactions), so that immediate-settlement is optimal, then perhaps it should take the form of small-denomination zero-interest paper. If record-keeping is economical (think large-value transactions), so that delayed settlement is optimal, then perhaps it should take the form of interest-bearing book-entry objects, like U.S. treasuries today). In any case, the question of what form this government debt should take is peripheral to the points stressed in this essay.

One of the benefits of government debt is that it may substitute for capital in the payments system. Think of U.S. treasuries substituting for mortgage-backed securities in the repo market, for example, or government paper notes (fiat money) substituting for capital-backed private banknotes. The effect of this substitution is to lower the "excess" demand on capital (contracting the level of elastic capital and lowering the price of fixed capital), thereby increasing the real rate of interest (closer to its natural rate).

In this manner, the introduction of government debt may lower the liquidity premia (bubbles) on private asset classes that serve as good collateral. It is interesting to note, however, that asset price bubbles do not disappear--rather, they are "exported" to government securities. The market price for fiat currency (the inverse of the price-level), for example, consists entirely of a liquidity premium (the fundamental value of fiat money is zero, so its value can only be supported by a bubble). To the extent that treasury debt is not fully backed by future taxes, a part of its value too may consist of a bubble that reflects its desirable properties as a collateral instrument (note: the use of U.S. treasuries in repo and credit derivatives markets has exploded over the last 30 years). In short, asset bubbles can be welfare-improving in a world of asset shortages (they may also come with their own set of problems, of course).

Information insensitivity

A concluding thought (sorry--I've already expressed too many for one post). Perhaps one reason why senior grades of debt are valued as exchange media relates not to their risk characteristics, but rather to debt's(relative) insensitivity to certain types of information. This is a theme that Gary Gorton likes to stress. One good property of a monetary instrument is that due diligence need not be performed on the object in each and every transaction. The institution of debt may be explained, in part, by the need to create instruments whose value is not subject to the speculation of informed insiders; see Gorton and Pennacchi 1990. Needless to say, government debt may be particularly attractive for this reason.

But even if information is not asymmetric, I point out here that not all information has social value. What this means is that if the efficient-markets-hypothesis holds (asset prices rapidly incorporate all information, whether such information has social value or not), asset prices may exhibit a form of "excess volatility." Private money instruments may not be able to avoid this excess volatility (in particular, the downside risk I talked about earlier). Now, one usually thinks of the unbacked nature of fiat money as a drawback. But on the other hand, representing a claim against nothing in particular may have its advantages. In particular, the return to fiat money is not directly linked to any information that relates to the underlying fundamentals of a private asset. What this means is that fiat money may possess social value to the extent that its return is insensitive to information of no social value. Some food for thought, at least. But enough for now.

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